论文标题
稳定流体运动中的灵活性和刚度
Flexibility and rigidity in steady fluid motion
论文作者
论文摘要
研究了Euler，Boussinesq和磁液压方程的稳定（时间无关）溶液的柔韧性和刚度性能。具体而言，建立了某些liouville型定理，表明没有停滞点的合适稳定溶液占据了二维周期通道或轴对称溶液（空心的）圆柱体，必须具有某些结构对称性。还表明，这种解决方案可以变形为占用域本身就是基本域的小扰动。作为一般方案的应用，Arnol'D稳定溶液在结构上是稳定的。
Flexibility and rigidity properties of steady (time-independent) solutions of the Euler, Boussinesq and Magnetohydrostatic equations are investigated. Specifically, certain Liouville-type theorems are established which show that suitable steady solutions with no stagnation points occupying a two-dimensional periodic channel, or axisymmetric solutions in (hollowed out) cylinder, must have certain structural symmetries. It is additionally shown that such solutions can be deformed to occupy domains which are themselves small perturbations of the base domain. As application of the general scheme, Arnol'd stable solutions are shown to be structurally stable.
